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- bobbym
- 2012-10-22 08:48:48
Hi;
I was just curious about the taylor series
What would you like to know?
- zetafunc.
- 2012-10-22 03:02:44
Sabbir wrote:
I was just curious about the taylor series
I mean, about the Gamma function -- is it for a particular class?
- Sabbir
- 2012-10-22 03:00:38
I was just curious about the taylor series
- bobbym
- 2012-10-22 02:52:18
You can also evaluate the integral numerically.
- zetafunc.
- 2012-10-22 02:47:19
Sabbir wrote:
So,will the taylor series give the same result as the integral's.
They will give you a (very good) approximation to the integral, yes.
May I ask what this is for?
- Sabbir
- 2012-10-22 02:41:30
So,will the taylor series give the same result as the integral's.
- zetafunc.
- 2012-10-22 02:14:44
Sorry, I am wrong.
. Ignore my previous post.- zetafunc.
- 2012-10-22 02:11:46
Evaluating it at complex numbers is interesting. Let's try to find Gamma(1+i).
but note that
so our integral becomes
I can do that becaues ei is just a constant. Can you see where to go from here?
- bobbym
- 2012-10-22 02:07:21
Those get very complicated. One way is with a Taylor series expanded around infinity.
This is quite close for only two terms of a Taylor series.
- Sabbir
- 2012-10-22 02:00:29
Ok,but it will be helpful to see a complex number example.
- zetafunc.
- 2012-10-22 01:56:24
There are lots of ways to compute values for the gamma function. For example, this is a useful identity;
Thus, since
then it follows that
so you can use that to find values of the gamma function at 5/2, 7/2, etc.
- bobbym
- 2012-10-22 01:53:05
Hi;
Only certain values yield nice results like that. For say Gamma(10 + 1/3 ) you will have to resort to numerical methods.
- Sabbir
- 2012-10-22 01:35:47
Yes,different values and your explanation was clear but other values will make it easier for me to understand the way of approaching
- zetafunc.
- 2012-10-22 01:10:02
You mean evaluating the gamma function at different values -- 0.75, 0.224, (3+2i), etc.?
Was any part of my explanation unclear?
- Sabbir
- 2012-10-22 01:07:05
I think if you show me some examples(such as other fractions and complex number)it will be easy for me to understand.